Normalize an angle and find its acute reference-angle relationship by quadrant.
Calculate
Enter values and calculate.
Result
Formula and method
The angle is normalized to [0, 360°) or [0, 2π). Quadrants use θ, 180°−θ, θ−180°, or 360°−θ respectively.
Worked example
150° is in Quadrant II, so its reference angle is 180° − 150° = 30°.
Limits and ownership boundary
A reference angle is defined here as an acute angle to the horizontal axis. Axis angles are reported explicitly as axis angles with an undefined reference angle; they are not assigned to quadrants.